Suppose a pitcher claims that his pitch speed is more than 4…

Suppose a pitcher claims that his pitch speed is more than 41 miles per hour, on average. Several of his teammates do not believe him, so the pitcher decides to do a hypothesis test, at a 5% significance level, to persuade them. He throws 29 pitches. The mean speed of the sample pitches is 45 miles per hour. The pitcher knows from experience that the standard deviation for his pitch speed is 3 miles per hour. H0: μ=41; Ha: μ > 41 α = 0.05 (significance level) What  is the test statistic (z-score) of this one-mean hypothesis test?

A zoologist is interested in whether climate affects how hig…

A zoologist is interested in whether climate affects how high kangaroos can jump. In a random sample of gray kangaroos from an Australian forest, he found the mean jump height was 286 inches with a margin of error of 25 inches. Construct a confidence interval for the mean jump height of gray kangaroos.

A recent study suggests that 74% of high school students buy…

A recent study suggests that 74% of high school students buy lunch. Olivia is a teacher at a high school who would like to know whether the percentage is more for high school students at her school. She randomly selects 50 students at her school and finds that 36 of the students buy lunch. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test?

Ethan wants to estimate the proportion of people in an airpl…

Ethan wants to estimate the proportion of people in an airplane who are over the age of 65. He surveys 324 airplane passengers and finds that 26 are over the age of 65. What is Ethan’s estimate for the proportion of people in an airplane who are over the age of 65?

The lengths of text messages have an unknown distribution wi…

The lengths of text messages have an unknown distribution with mean 26 and standard deviation 5 characters. A sample, with size n = 40, is randomly drawn from the population and the mean is taken. What is the probability that the mean is more than 24.5 characters?